We prove that the mass of asymptotically flat manifolds of nonnegative scalar curvature is lower semicontinuous under pointed C^0 convergence. Since the limit need not be smooth, we use Huisken’s isoperimetric mass, which generalizes the usual ADM mass. Our approach requires some new facts about Huisken’s quasilocal isoperimetric mass, which we prove using a modified version of weak mean curvature flow. This is joint work with Jeff Jauregui.